GSTARIX Model for Forecasting Spatio-Temporal Data with Trend, Seasonal and Intervention

Abstract

Generalized Space-Time Autoregressive (GSTAR) is a statistics model that usually applied for forecasting data that have both spatial and temporal dependency. The monthly tourist arrival data in some locations are example of spatio-temporal data. Most of previous researches in GSTAR model only focused on stationary data. Otherwise, tourist arrival data in Indonesia mostly contain trend, seasonal, and some extreme values caused by interventions or outliers. The objective of this study is to apply and develop GSTAR model for forecasting spatio-temporal data with trend, seasonal, and interventions or outliers. This model is then known as GSTAR with exogeneous variables or GSTARIX model. Then, the forecast accuracy of GSTARIX model are compared to VAR with exogenous variables or VARIX model. Monthly data about number of tourist arrivals to Jakarta, Surakarta, Surabaya, and Denpasar are used as case study. Moreover, two methods are used for parameter estimation, i.e. Ordinary Least Square (OLS) and Generalized Least Square (GLS). The criteria for selecting the best model is Root Mean Square Error (RMSE). The results showed that the best model for forecasting tourist arrivals in each location are different. The best model for forecasting number of tourist arrivals to Jakarta and Surabaya is GSTARIX with OLS method or GSTARIX-OLS. Whereas, the best model for Denpasar and Surakarta data are VARIX and GSTARIX-GLS, respectively.